The exponent \(\beta \)  = 0.6 is close to 1/\(T_1\propto \sqrt{T}\)  for the non-degenerate Fermi gas with \(T > \it \Delta \)  [1]}, [2]}.
Theoretically, the degenerate Fermi gas at \(T < T_\mathrm {F}\)  (the Fermi temperature) yields the Korringa law, while the non-degenerate Fermi gas at \(T > T_\mathrm {F}\)  yields 1/\(T_1\propto \sqrt{T}\)  according to the electron density of states \(\rho (E)\propto \sqrt{E}\)  [1]}, [2]}.
However, no report of 1/\(T_1\propto \sqrt{T}\)  has been found on actual semiconductors.
For doped Si:P semiconductors, 1/\(T_1\propto T^{1.6}\)  was reported [5]}.
